Question

Use the information listed below to solve parts a through h Suppose that the demand and price for a certain model of a youth wristwatch are related by the following equation, where p is the price (in dollars) and q is the quantity demanded (in hundreds). \( \mathrm{p}=\mathrm{D}(\mathrm{q})=24-1.25 \mathrm{q} \) Find the price at each level of demand. Answer parts a through d.

Ask by Willis Coles. in the United States
Feb 18,2025

Upstudy AI Solution

Tutor-Verified Answer

Answer

When \( q = 0 \), \( p = 24 \) dollars; when \( q = 1 \), \( p = 22.75 \) dollars; when \( q = 2 \), \( p = 21.50 \) dollars; when \( q = 3 \), \( p = 20.25 \) dollars.

Solution

To solve the problem, we will use the demand equation given: \[ p = D(q) = 24 - 1.25q \] where \( p \) is the price in dollars and \( q \) is the quantity demanded in hundreds. ### Part a: Find the price when \( q = 0 \) Substituting \( q = 0 \) into the demand equation: \[ p = 24 - 1.25(0) = 24 \] So, when \( q = 0 \), the price \( p \) is **$24**. ### Part b: Find the price when \( q = 1 \) Substituting \( q = 1 \) into the demand equation: \[ p = 24 - 1.25(1) = 24 - 1.25 = 22.75 \] So, when \( q = 1 \), the price \( p \) is **$22.75**. ### Part c: Find the price when \( q = 2 \) Substituting \( q = 2 \) into the demand equation: \[ p = 24 - 1.25(2) = 24 - 2.5 = 21.5 \] So, when \( q = 2 \), the price \( p \) is **$21.50**. ### Part d: Find the price when \( q = 3 \) Substituting \( q = 3 \) into the demand equation: \[ p = 24 - 1.25(3) = 24 - 3.75 = 20.25 \] So, when \( q = 3 \), the price \( p \) is **$20.25**. ### Summary of Results - When \( q = 0 \), \( p = 24 \) - When \( q = 1 \), \( p = 22.75 \) - When \( q = 2 \), \( p = 21.50 \) - When \( q = 3 \), \( p = 20.25 \) If you have further parts (e through h) to solve, please provide them!

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Sure! Let's solve the parts step by step. a) To find the price when the quantity demanded is 0 (the base case): \[ p = D(0) = 24 - 1.25(0) = 24 \] So, when no watches are demanded (\( q = 0 \)), the price is $24. b) Now, let's find the price when the quantity demanded is 2 (which is 200 watches since \( q \) is in hundreds): \[ p = D(2) = 24 - 1.25(2) = 24 - 2.5 = 21.5 \] When the demand is 200 watches, the price drops to $21.50. c) Next, we'll calculate the price when the quantity demanded is 4 (which is 400 watches): \[ p = D(4) = 24 - 1.25(4) = 24 - 5 = 19 \] At a demand of 400 watches, the price further lowers to $19. d) Finally, let's find the price when the quantity demanded is 10 (or 1000 watches): \[ p = D(10) = 24 - 1.25(10) = 24 - 12.5 = 11.5 \] When the demand hits 1000 watches, the price goes down to $11.50. So, to summarize the findings: - When \( q = 0 \), \( p = 24 \) - When \( q = 2 \), \( p = 21.5 \) - When \( q = 4 \), \( p = 19 \) - When \( q = 10 \), \( p = 11.5 \)

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